Ever increasing economic demands require that components and structures have high reliability. It is usually the case that similar components experience large variations in their total life. For example, one machine element may last many years, yet another element produced by the same manufacturer may fail in a few months. Traditional design methods account for large uncertainty or scatter in life by using design safety factors. Low probabilities of failure can usually be ensured only by applying large safety factors during component design. But safety factors can add unnecessary redundancy, weight, and cost to a component because the true safe life of the component may be much greater than the predicted safe life. Furthermore, to ensure safety, components are often retired well before the useful lifetime is exhausted to insure that no component fails during operation (i.e. Aircraft parts). Designing cost effective and highly reliable structures and maximizing part life therefore requires the ability to accurately assess a component's safe life.
Assessing a component's safe life often requires determining the effects of fatigue on a component. Fatigue can occur in any device that has moving components. Fatigue can also occur in cases where the movement is imperceptible as do, for example, bridge elements or railroad tracks. Components also often fail in an insidious manner, giving no prior indication that damage has occurred. In the case of an aircraft engine, for example, such fatigue failures can be catastrophic.
Failure analysis has revealed that actual component loadings are often well below the steady loads that can cause failure. What distinguishes these failures is the fact that the loads have been applied a large number of times. Fatigue, more specifically fatigue crack initiation and growth, is therefore a damage mechanism that degrades the reliability and safe life of components subjected to repeated loads. Designing for fatigue is difficult because it typically exhibits a large variation in its effect on similar components.
In the case of fatigue failure, scatter in life is indicated by a coefficient of variation (COV) which is usually determined based on a wide range of fatigue life tests on many similar specimens. Even under well controlled laboratory tests of annealed smooth specimens at room temperature the COV varies from less than 10% to over 500% for different steel alloys. Thus, the considerable scatter in the fatigue reliability of components in operation may be substantially attributed to considerable scatter of component material fatigue behavior.
Life scatter is due to the fact that, in general, materials have inhomogeneous microstructures. To the naked eye, it may appear that a material is composed of continuous homogeneous material. Microscopic examination reveals, however, that metals, for example, are comprised of a discontinuous inhomogeneous material consisting of individual crystalline grains, pours, and defects. Cracks nucleate and grow on the order of grain size according to the properties of the individual grains, with growth rate as varied as grain properties. As these cracks grow the rate and behavior of the crack approaches the bulk or average properties of the material. Therefore, for large cracks, traditional crack growth methods are appropriate. Traditional methods, however, fail to determine the probability of crack initiation or to describe crack growth of near-grain-sized cracks. In many applications failure can occur before the fatigue damage reaches the long crack stage because the energy associated with the damage is very high although the damage is very small.
Current fatigue life prediction methods in metallic components consider three stages: crack initiation, long crack propagation, and final fracture. Long crack propagation and final fracture are stages of damage accumulation that are well characterized using computational models such as linear elastic or elastic-plastic fracture mechanics.
Crack initiation is the early stage of damage accumulation characterized by small cracks; cracks with depths less than several grain diameters. These have been observed to deviate significantly from predicted long crack fracture mechanics. The deviation is attributed to the heterogenous material in which small cracks evolve. The crack initiation phase accounts for the majority of scatter in fatigue life for many alloys. The crack initiation stage contains two phases: crack nucleation and small crack growth.
Crack nucleation is a locally complex process of crack formation on the microstructural scale. One example of a crack nucleation mechanism is the smooth fracture at angles inclined to the loading direction that is exhibited by materials having a propensity for planar slip. Crack growth is the similarly complex process that occurs once a crack has been nucleated.
Current crack initation models are based on empirical testing. This causes crack initiation models to be simple parametric functions of applied stress variables. As such, these macrostructural models assume the material to be homogeneous and continuous. Statistical concepts have been used to develop empirical fatigue life models where the independent variable, usually applied global stress or strain, is considered deterministic and the dependent variable, usually life, is considered random. But these models do not account for the mechanisms of the microstructural parameters that regulate fatigue damage. Since this major source of scatter (i.e. microstructural crack initiation, which includes both crack nucleation and small crack growth) is not included in these models, they are necessarily unsatisfactory because they cannot represent the heterogeneous material in which the damage processes occur.
Because traditional crack initiation models are empirical, they cannot represent conditions not included in the established database test program. Sequential variation is one such condition. Sequential variation is due to the component being used for many different scenarios. For example, an automobile is driven differently during each trip and an unlimited number of sequential variations would have to be considered. While current long crack growth propagation models are able to account for sequential variation in the component usage, it is not practical from a time and cost standpoint to include sequential variations in the applied stress under most test programs. Therefore crack initiation tests are generally conducted at a maximum i.e., “worst case”, stress to ensure safety. Thus components are generally systematically over-designed assuming unlikely worst case material properties to compensate for the lack of true understanding of the material fatigue behavior. Additionally, these traditional models are unsatisfactory for predicting individual component failure because the vast majority of components by definition do not possess these unlikely worst case material properties. Predictions made using such models are based upon the worst case material properties and are thus inaccurate.
FIG. 1 depicts three levels of fatigue damage that may occur in a typical high strength component. First, a crack nucleates 200 on a small scale on the order of the grain size. Then the crack grows as a microscopically small crack 202 in which the crack lies in relatively few grains. The material properties, averaged along the front of the crack, approach bulk or average material properties as the crack grows and the number of grains intercepted by the crack front increase. When the material properties intercept enough grains traditional crack growth techniques such as linear elastic fracture mechanics 204 may be applied. But the majority of crack life is spent in the nucleation and small crack growth regime for high strength components. Thus, understanding the early crack behavior is most important. As a result, there exists a need for a method and apparatus for accurately predicting component failure that account for the microstructural properties of materials and sequential variation in the loading, and relate them to fatigue scatter.